SURFACE AND INTERNAL CRACKS IN A RESIDUALLY STRESSED PLATE

The problem of a surface or an internal crack in a plate which contain s residual stresses is examined. The line spring model, which reduces a three-dimensional elasticity problem into a two-dimensional problem in plate theory, is used to model the crack. The Reissner plate theory , which takes into account transverse shear deformations, is used to m odel the plate. The formulation is based on Fourier Transforms which l ead to a pair of singular integral equations that are solved numerical ly. The line spring method requires the plane strain solution to both the edge and internally cracked strip with crack surface loads represe ntative of tension, bending, and the given residual stress distributio n. For general use, plane strain solutions are presented for polynomia l loading through the thickness up to the fifth order. Comparisons are made between the results given by the line spring model for the Reiss ner plate theory and the finite element method.